The victims were held up to four months in the house after being snatched from buses or bus terminals, while their captors demanded ransom money for their release.
Police followed the alleged captors to the building at the edge of the city of Reynosa, where they heard frantic cries for help.
The northwestern state Tamaulipas, where Reynosa is located, is one of the most violent regions of Mexico. The city borders McAllen, Texas.
Six minors were among the ones rescued. Several of the victims claimed to have been sexually abused while in captivity.
Police confirmed that the 73 victims in the house came from four countries: 19 Hondurans, 14 Guatemalans, three Salvadorans and 37 Mexicans. Police have identified and held three suspects.
They also seized weapons and drugs from the property, including a grenade and nearly 10,000 kilograms of marijuana.